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Cascade Step Chimes

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Ever stood by a cascading waterfall and heard the musical ring of bronze chimes? That’s the magic of Cascade Step Chimes! In this ritual, the number of chimes grows as you move down every terrace. It starts with one base chime, and for each new step, a new guiding chime is added while the entire previous soundscape triples through stone echoes.

The "secret sauce" here is a mathematical Recurrence Pattern. Specifically, the total number of chimes follows the formula f(n) = 2 × 3ⁿ - 1, where n is the number of terraces after the initial landing. As the number of steps increases, the soundscape grows exponentially, creating a rich, layered chorus that fills the Silvervein Falls. Your goal is to calculate this precise total so the musicians can maintain the perfect harvest festival structure.

This challenge is a brilliant way to practice modeling exponential growth with simple integer math. It’s a leap from simple counting to understanding how patterns can explode in complexity with just a few rules!

Examples

Example 1
Input
steps = 4
Output
161
Explanation

Four additional steps mean another guiding chime plus a tripled echo of everything below, totaling 161 chimes.

Example 2
Input
steps = 0
Output
1
Explanation

Only the base chime plays, so the crowd hears a single note.

Example 3
Input
steps = 2
Output
17
Explanation

The second step adds one guiding chime and repeats the prior soundscape three times, ending with seventeen chimes.

Algorithm Flow

Recommendation Algorithm Flow for Cascade Step Chimes - Budibadu
Recommendation Algorithm Flow for Cascade Step Chimes - Budibadu

Best Answers

java
class Solution {
    public int count_chimes(int steps) {
        return 2 * (int) Math.pow(3, steps) - 1;
    }
}